Magnetic eigenmodes in chains of coupled $\varphi_0$-Josephson junctions with ferromagnetic weak links

A coupled chain of superconductor/ferromagnet/superconductor (S/F/S) with anomalous ground phase shift ${{\varphi }_{0}}$ represents a system realizing long-range interaction between magnetic moments of the weak links. The interaction is of magnetoelectric origin and is mediated by the condensate phase of superconductors. The system is a paradigmic platform for investigation of collective magnetic states governed by the superconducting phase. Here we study the magnetic eigenmodes of such a system and demonstrate that the eigenfrequencies are determined by the magnetic configuration of the whole system and are controlled by the superconducting phase. Depending on the orientation of the magnetic easy axis the eigenmodes can be very different ranging from individual oscillations of different magnets to highly-cooperative behavior.